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A car on the cross road is moving towards east at a speed of 40km/hr. Another car which is 1 km south of crossing is approaching the crossing with the same speed . Their closest distance of approach will be ?
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Calculation of the Closest Distance of Approach between Two Cars on Cross Road


Given Information


  • Speed of the first car moving towards east = 40 km/hr

  • Speed of the second car approaching the crossing = 40 km/hr

  • Distance between the second car and crossing = 1 km



Calculation


  • Let's assume that the two cars meet at a point P which is the closest distance of approach.

  • Let's also assume that the first car takes t hours to reach the crossing from its initial position and the second car takes T hours to reach the crossing from its initial position.

  • Then, the distance covered by the first car = 40t km and the distance covered by the second car = 40T km.

  • Using Pythagoras theorem, the distance between the initial position of the second car and point P is given by:


    • √(1^2 + (40T)^2)


  • Similarly, the distance between the initial position of the first car and point P is given by:


    • √((40t)^2 + 0^2)


  • As the two cars meet at point P, the above two distances must be equal.

  • Therefore, we can write:


    • √(1 + 1600T^2) = 40t


  • Squaring both sides, we get:


    • 1 + 1600T^2 = 1600t^2


  • Bringing all the terms to one side, we get:


    • 1600t^2 - 1600T^2 = 1


  • Dividing both sides by 1600, we get:


    • t^2 - T^2 = 0.000625


  • Factoring the left-hand side, we get:


    • (t - T)(t + T) = 0.000625


  • As t and T are positive, we can ignore the negative solution.

  • Therefore, we can write:


    • t - T = 0.025


  • Substituting this value of (t - T) in the equation we got earlier, we get:


    • t^2 - (t - 0.025)^2 = 0.000625


  • Simplifying this equation, we get:


    • t =
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A car on the cross road is moving towards east at a speed of 40km/hr. Another car which is 1 km south of crossing is approaching the crossing with the same speed . Their closest distance of approach will be ?
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